On equational theories, unification, and (Un)decidability

Unification and Anti-unification modulo Equational Theories

Automated reasoning modulo an equational theory E is a fundamental technique in many applications. If E can be split as a disjoint union R ∪ Ax in such a way that R is a set of rewrite rules that are confluent, terminating, sort-decreasing, and coherent modulo a set of equational axioms Ax, it is well-known that narrowing with R modulo Ax provides a complete E-unification algorithm. However, na...

On Equational Theories, Unification and Decidability

The following classes of equational theories, which are important in unification theory, are presented: permutative, finite, Noetherian, simple, almost collapse free, collapse free, regular, and ~-free theories. The relationships between the particular theories are shown and the connection between these classes and the unification hierarchy is pointed out. We give an equational theory that alwa...

On Equational Theories, Unification, and (Un)Decidability

We investigate the following classes of equational theories which are important in unification theory: permutative, finite, Noetherian, simple, almost collapse free, collapse free, regular, and O-free theories. We show some relationships between the particular classes and their connections to the unification hierarchy. Especially, we study conditions, under which minimal and complete sets of un...

Universal Unification and Regular Equational ACFM Theories

Unification in Extension of Shallow Equational Theories